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Wednesday, 18 August 2010

I have some papers I wanted to talk about, but it occurred to me that they only make sense in a context. So I'm going to spend some time talking about the experimental task I use a lot, why it's interesting and what we can learn from it about perception and action.

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To a man with a hammer, everything looks like a nail. My hammer is coordinated rhythmic movement, and I use it to study everything I'm interested in - perception-action, learning, ageing, you name it. This task is a workhorse of the perception-action literature and has been since Kelso described it in 1981 (after the task was, as far as I can find, first described by Cohen, 1971).

The reason this task is used so widely is simple - it's easy to study and it's surprisingly interesting. Take the canonical example from Kelso:extend the index finger of each hand, and oscillate them up and down at a comfortable frequency and with the same amplitude. You can move these fingers independently and have them do anything you like; it gets interesting when you try to coordinate their behaviour, i.e. have them move in some fashion with respect to one another. Move them so they do the same thing at the same time: this is in-phase motion and you can likely do this all day if need be. Now alternate them so that one moves up as the other moves down: this is anti-phase motion and you can also do this all day, unless I ask you to speed up and not resist any urge to change what you're doing ('non-interference' instruction). Your movements will become less stable as frequency increases (the standard deviation of phase, or phase variability, increases). Around 3-4Hz most people will switch from anti-phase to in-phase and the phase variability will drop down to below the critical value that triggered the urge to switch in the first place.

Now try to produce the intermediate, syncopated rhythm. When one finger is at one extreme the other should be halfway through it's motion from one extreme to the other. You may be able to do this if you move fairly slowly, but as soon as you try to speed up you will likely lose the rhythm (unless you are, for example, a drummer).

It turns out that people have tremendous difficulty maintaining any rhythm other than in- or anti- phase, with that intermediate case being the hardest. This is quite astonishing - for some reason, the attempt to coordinate two extremely simple movements seems to pose a serious problem for the perception-action system. What could possibly be the reason?

Before we get into the theories, let's get a few definitions out of the way. The word 'phase' came up - what does this mean?

Figure 1. The relationship between the motion in the world, and the representation of the motion in phase space; click to see it animated if it's not displaying correctly.

Rhythmic movements are those that repeat a pattern over time. A finger moving up and down through one cycle produces a sinusoidal position time series; however, if all you measure is position (which is the most commonly directly measured kinematic variable) then you already have a problem, because the finger occupies the same position (say, the halfway point) twice, once on the way up, once on the way down. Position does therefore not provide use with a unique number for each location in the cycle. The difference between the two identical positions is the direction you're moving: direction, combined with speed, is velocity and numerically is the sign (+ or -) of the speed magnitude. If we have these two numbers (position and velocity) we can uniquely identify each location in the cycle, but two numbers are always less use than one when describing a movement.

Phase is 'position in a cycle', and is the angle created by a line drawn from the origin of a plot of position vs. velocity (the point 0,0) to the current (position, velocity) coordinate. This angle is a single number than ranges from 0° to 360° (or 0 to 2π radians) and it uniquely identifies every location in the cycle. By convention, to simplify the maths, the position data is normalised by the amplitude of motion, and the velocity data is normalised by the frequency; by trigonometry, phase is therefore the inverse tangent of velocity divided by position.We have simply combined position and velocity into a single, useful number.

Coordinated rhythmic movements entail two of these moving with respect to one another. We now have two phases, one for each limb: to get back to one number, we compute the difference - relative phase. If they are doing the same thing at the same time (in-phase) then the difference between the angles is 0°; if they are doing the opposite thing, the difference is 180°; and the syncopated intermediate rhythm has a mean relative phase of 90°.

We know have a single number, relative phase, that measures the coordination between two oscillating things, like fingers. In the next post, we'll look at the first descriptions of how behaviour varies with mean relative phase and how that can be modelled.